# Bubble Math: Researchers Describe Mathematically the Stages in Bubble Evolution

Posted on May 10, 2013

Researchers from University of California, Berkeley have described mathematically the successive stages in the complex evolution and disappearance of foamy bubbles. The mathematicians, James A. Sethian and Robert I. Saye, came up with equations that work for large bubble clusters.

The researchers say solving the full set of equations of motion took five days using supercomputers at the LBNL's National Energy Research Scientific Computing Center (NERSC).

Saye said in a statement, "This work has application in the mixing of foams, in industrial processes for making metal and plastic foams, and in modeling growing cell clusters. These techniques, which rely on solving a set of linked partial differential equations, can be used to track the motion of a large number of interfaces connected together, where the physics and chemistry determine the surface dynamics."

The mathematicians also created this computer-generated video of a cluster of bubbles popping out of existence. The video shows liquid draining from the bubbles' thin walls until they rupture. The remaining bubbles then rearrange, which often destabilizes other bubbles, which subsequently pop.

Take a look:

The bubble mathematics research was published here in the journal,

*Science*.

Image: UC Berkeley